I belong to a progressive Church. We are Catholics, but we believe that the current positions of the Vatican on things like women's ordination, celibacy, and gay rights are erroneous interpretations of the divine instruction contained in the Bible. My manager is a member of a traditional Catholic Church, and we have discussed religion on occasion. He has begun making pointed comments to me about my beliefs, telling me that I'm not a true Catholic, that I can't just change the rules if I don't like them, questioning my belief in God, and so on. It's gotten to a point where every time we meet, it devolves into him questioning my religious beliefs. I finally told him that I was starting to feel harassed because of my religion; he countered that my beliefs aren't religious because they diverge from the Church's current doctrine, so he can say whatever he wants. Do I have any rights here?
You have a right to work free from harassment based on your religious beliefs. So there are two questions here: Are your beliefs religious? And if so, does your manager's behavior amount to harassment?
The answer to the first question is yes. Employees are protected from discrimination and harassment based on their religious beliefs (or lack thereof). An employee need not belong to a traditional, mainstream religion to be protected; sects, offshoots, and small groups are also covered. Even employees whose religious beliefs diverge from the teachings of the faith to which they claim allegiance are protected. So, you are protected from discrimination, even if your beliefs differ in some respects from the official doctrine of the Catholic Church.
The answer to the second question is that it depends. Workplace conduct or statements based on a protected category (in this case, your religion) cross the line to become harassment if they are unwelcome and they create an intimidating, hostile, or offensive work environment. For certain types of harassment, a single incident may be enough to cross the line. For example, if an employee physically assaults another employee or uses extremely offensive language, that is likely sufficient. For other types of harassment, the conduct must be sufficiently persistent and offensive to alter your working conditions. It's difficult to say whether your situation has reached this level, but it may have. If you cannot meet with your manager without having to put up with these demeaning comments, and he hasn't stopped despite your requests, that might be enough to show harassment.
Generally, the first step anyone facing harassment should take is to ask the harasser to stop. It sounds like you've already done that, but try one more time. Rather than arguing over whether you are really a Catholic or whether his comments add up to legally actionable harassment, simply tell him that you find his comments offensive and you would like him to stop. If this doesn't work, go to your company's HR department and make a complaint. Hopefully, your company will investigate and put a stop to your manager's behavior.
Many problems are resolved at this stage, without any need to go outside the company. If yours is not, however, you'll need to decide whether to pursue legal action. This is a very good time to talk to an experienced employment lawyer, who can help you assess your chances in court (including any damages that might be available to you) and decide how you want to proceed. If your workplace situation continues to deteriorate (for example, your manager begins downgrading your performance, demotes you, or even fires you), it might be worth taking the next step, which is filing a charge of harassment with the Equal Employment Opportunity Commission or your state's fair employment practices agency.